Uniqueness of Smooth Stationary Black Holes in Vacuum: Small Perturbations of the Kerr Spaces
Uniqueness of Smooth Stationary Black Holes in Vacuum: Small Perturbations of the Kerr Spaces
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DOI：
10.1007/s00220-010-1072-1
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发表时间：
2010-10-01
影响因子：
2.4
通讯作者：
Klainerman, S.
中科院分区：
文献类型：
--
作者：
Alexakis, S.;Ionescu, A. D.;Klainerman, S.
本文的目的是证明一个微扰的结果，关于Kerr解的唯一性，我们相信这一结果将是有用的证明其非线性稳定性。在Ionescu和Klainerman（发明。175：35-102，2009），我们试图去除著名的Hawking-Carter-罗宾逊唯一性结果中的解析性假设。不像（Ionescu和Klainerman在发明。175：35-102，2009），其基于Kerr解的张量表征，由于Mars（Class.定量重力16：2507-2523，1999），我们在这里依赖于霍金的原始策略，这是将一般静止时空的情况减少到卡特-罗宾逊唯一性结果成立的静止和轴对称时空的情况。在这种还原中，霍金不得不诉诸分析性。使用一个变量的几何Carleman估计开发的Ionescu和Klainerman（发明。175：35-102，2009），在本文中，我们展示了如何在稳态真空时空是给定克尔解的小扰动的情况下绕过解析性。我们的扰动假设表示为一个统一的小条件的Mars-Simon张量。我们证明的出发点是Alexakis等人建立的新的局部刚性定理（Hawking's local rigidity theorem without analyticity）。http：//arxiv.org/abs/0902.1173v1 [gr-qc]，2009年）。
The goal of the paper is to prove a perturbative result, concerning the uniqueness of Kerr solutions, a result which we believe will be useful in the proof of their nonlinear stability. Following the program started in Ionescu and Klainerman (Invent. Math. 175:35-102, 2009), we attempt to remove the analyticity assumption in the the well known Hawking-Carter-Robinson uniqueness result for regular stationary vacuum black holes. Unlike (Ionescu and Klainerman in Invent. Math. 175:35-102, 2009), which was based on a tensorial characterization of the Kerr solutions, due to Mars (Class. Quant. Grav. 16:2507-2523, 1999), we rely here on Hawking's original strategy, which is to reduce the case of general stationary space-times to that of stationary and axi-symmetric spacetimes for which the Carter-Robinson uniqueness result holds. In this reduction Hawking had to appeal to analyticity. Using a variant of the geometric Carleman estimates developed in Ionescu and Klainerman (Invent. Math. 175:35-102, 2009), in this paper we show how to bypass analyticity in the case when the stationary vacuum space-time is a small perturbation of a given Kerr solution. Our perturbation assumption is expressed as a uniform smallness condition on the Mars-Simon tensor. The starting point of our proof is the new local rigidity theorem established in Alexakis et al. (Hawking's local rigidity theorem without analyticity. http://arxiv.org/abs/0902.1173v1[gr-qc], 2009).